Rishi Sunak had 101 votes and Penny Mordaunt 83 as Suella Braverman was eliminated from the contest after the second round of voting.
Secretária estrangeira Liz Truss came in third but will hope to pick up votes from Ms Braverman’s supporters in the next round.
Mr Sunak picked up 101 votos, Senhora Mordaunt 83, Senhora Truss 64, Kemi Badenoch 49 and Tom Tugendhat 32.
Ms Braverman had 27 votos, five fewer than she had in Wednesday’s first round of the contest despite the field being smaller on Thursday.
Mr Tugendhat also dropped five votes but insisted he would not quit the race, dizendo: “I have never turned down a challenge because the odds were against me. I don’t plan to start now.”
Ms Mordaunt gained the most votes, putting on 16 from Wednesday’s total.
Mr Sunak put on an extra 13 votes and is closing in on the 120 votes required to guarantee a place in the final two, who will face a vote of the Tory membership to decide the next party leader and prime minister.
Senhora Truss, who had a campaign launch speech earlier on Thursday, ganhou 14 votes but will hope that she can serve as a standard-bearer for the party’s right, picking up supporters from not only Ms Braverman but also Ms Badenoch – who is under pressure from the Foreign Secretary’s allies to pull out of the contest.
Secretário de cultura Nadine Dorries, a Truss supporter, disse: “Now is the time for us all to unite behind a candidate who actually has the ability to lead the country as PM.”
The contest became particularly vicious on Thursday, with allies of Ms Truss seizing on comments from former Brexit minister Lord Frost about Ms Mordaunt’s competence.
He told TalkTV: “She was my deputy – notionally, more than really – in the Brexit talks last year.
“I felt she did not master the detail that was necessary in the negotiations last year. She wouldn’t always deliver tough messages to the European Union when that was necessary.
“She wasn’t fully accountable, she wasn’t always visible. Sometimes I didn’t even know where she was. This became such a problem that, after six months, I had to ask the Prime Minister to move her on and find somebody else to support me.”
Allies of Ms Mordaunt said she had “nothing but respect” for Lord Frost despite his scathing attack on her.
A source in the Mordaunt campaign said: “Penny will always fight for Brexit and always has.”
But the former minister’s remarks were highlighted by the Truss campaign, with Treasury Chief Secretary Simon Clarke dizendo: “Lord Frost’s warning is a really serious one. Conservatives – and far more importantly our country – need a leader who is tested and ready.”
Mr Clarke told Sky News: “It is telling, eu acho que, where current members of the Government are placing their support.
“That is reflected in a number of very senior ministers’ decisions about who to support in this race – they are not backing Ms Mordaunt.”
Former cabinet minister David Davis, a supporter of Ms Mordaunt, criticised the “black ops” being directed at her.
“I wouldn’t describe it as friendly fire," ele disse. “It’s absolutely clockwork – you get to the point that somebody gets ahead and looks to be the real challenger and then the black op starts, the incoming fire starts.”
Enquanto isso, Mr Sunak insisted his wealth and background in international finance do not bar him from understanding the plight of hard-pressed households.
Ele disse ao programa Today da BBC Radio 4: “I don’t judge people by their bank accounts, I judge them by their character, and I think people can judge me by my actions over the past couple of years.”
Mr Sunak defended his economic plan, which would not involve the immediate tax cuts promised by his rivals.
“I will get taxes down in this Parliament, but I’m going to do so responsibly," ele disse.
“Because I don’t cut taxes to win elections, I win elections to cut taxes, and I’m convinced that I’m the best person to beat Keir Starmer and the Labour Party at the next election.”
Mr Clarke, who was Mr Sunak’s ministerial deputy in the Treasury, disse: “We were all frustrated by some of the choices in terms of tax, obviously those are private discussions in Government when we were bound by collective responsibility.
“But I’m clear I favour a low-tax, pro-enterprise economy and I think Liz Truss has the right approach on that.”
Canal 4 said all five candidates have confirmed they will take part in its debate on Friday night, with further televised clashes scheduled for Sunday and Monday.
The next round of voting is due on Monday, with subsequent rounds if required until two candidates are left, who will then battle it out over the summer to win the support of Conservative members. Their choice of the next prime minister will be announced on September 5.
Boris Johnson will then formally tender his resignation to the Queen to make way for his successor the following day.